The correct relationship among the following, for a tetragonal (a = b ≠ c, α = β = γ = 90°) crystal system, is · ABC26PH0190
Subject: Physical Chemistry · Chapter: Solid State Chemistry · Topic: Crystal Systems Lattices · Exam: CSIR NET 2019 · Marks: 2 · Difficulty: Medium
The correct relationship among the following, for a tetragonal ($a = b \neq c$, $\alpha = \beta = \gamma = 90^\circ$) crystal system, is
(a)$\sin^2\theta = \frac{\lambda^2}{4a^2}\left[c^2(h^2 + k^{2b}) + a^2 l^2\right]$
(b)$\sin^2\theta = \frac{\lambda^2}{4a^2c^2}\left[c^2(h^2 + k^{2b}) + a^2 l^2\right]$
(c)$\sin^2\theta = \frac{\lambda^2}{4c^2}\left[a^2(h^2 + k^2) + c^2 l^2\right]$
(d)$\sin^2\theta = \frac{\lambda^2}{4a^2}(h^2 + k^2) + l^2]$
Answer
Explanation
From braggs equation , 2d sin 𝜃 =n λ £‡ si𝑛𝜃 = <‘ On squaring both sides , we get £ 0 ‡0 si𝑛< 𝜃 = ………(i) H‘ 0 # M0 …0 l0 inter planar distance = + 0 + 0 ‘0 /0 à N for tetragonal crystal sydrem , a = b ≠ 𝑐 # M 0 1… 0 l0 N 0 M 0 1… 0 1l 0 / 0 0 = + 0 ⇒ ‘ /0 N /0 N 0 # ‡0 Put in equation (i), we get 𝑠𝑖𝑛< 𝜃 = [𝑎< ℎ< + 𝑘 < + 𝑐 < 𝑙 < ] ‘0 HN 0 𝒂
Explanation as extracted from the printed page; notation may be imperfect.
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